In many modem communication systems, information is transmitted and received by modulating a radio frequency (RF) carrier signal with a data signal and then demodulating the RF signal to recover the data signal. Demodulating an RF carrier signal usually involves tuning a receiver to the carrier signal, which may be at a substantially higher frequency than the frequencies of the data it conveys. For example, a carrier signal frequency may be on the order of 1-2 GHz, whereas the bandwidth of the data channel conveyed by the carrier signal may be on the order of only 100-200 kHz.
In one approach to demodulating an RF signal, a bandpass filter having a bandwidth approximately equal to the data channel bandwidth may be tuned to the RF carrier signal frequency, and the filter output may be demodulated according to the original modulation scheme. However, narrow-bandwidth bandpass filters become increasingly difficult and bulky to implement as their center frequencies increase. Consequently, many RF receiver systems use some form of heterodyning to convert a received RF signal to a lower frequency (referred to as an intermediate frequency, or IF), where the task of filtering may be easier.
Generally speaking, heterodyning a signal involves mathematically multiplying one signal, such as an RF signal, with a second signal close in frequency to the first, often referred to as a local oscillator (LO). Such an operation, also referred to as mixing, results in signals at frequencies equal to the sum and difference of the RF frequency and the LO frequency. The sum frequency is usually substantially higher than the RF or LO frequency and may be readily filtered using a simple low-pass filter. The difference frequency is the IF frequency, which is usually close to DC and is therefore readily manipulated by simple filters.
Typical heterodyne systems are susceptible to a phenomenon referred to as imaging. As described above, a given desired RF frequency fRF differs from a given LO frequency fLO by the IF frequency fIF. Further, a given desired RF frequency may lie either above or below the LO frequency. However, due to its symmetric properties, heterodyning will select any RF signal differing from fLO by fIF, irrespective of whether the RF signal lies above or below the given LO frequency. For example, if a desired RF signal is at 1.01 GHz and the LO signal is at 1.00 GHz, mixing the two signals results in an IF of 10 MHz. However, if another RF signal is present at 990 MHz, this signal will also be translated to the 10 MHz IF, which may result in interference with the information content of the desired RF signal. In heterodyne systems generally, for a given RF signal of frequency fRF=fLO±fIF, the frequency fimage=fLO∓fIF may be referred to as the image frequency.
To prevent interference with the desired RF signal, the image frequency may be filtered prior to heterodyne mixing. However, as noted above, such a filter may be difficult to implement, which is a primary motivation for implementing a heterodyne system. In some systems, quadrature receiver architectures may be employed that facilitate image frequency rejection by splitting the desired RF signal into two paths and mixing each path with a respective function of the LO signal, where the respective functions may have a particular phase relationship (such as sine and cosine functions). However, imbalances in gain and phase relationships between the two paths may yield imperfect image frequency rejection, resulting in undesired interference that may require further filtering or correction.